Hello Hobart and welcome to the forum!!
I play euphonium and trombone (both tenor and bass), and I also play a little tuba. Since trombone is your main instrument, going with an Eb tuba may be the easiest transition, at least for the mouthpiece size. Wessex offers quite a few tubas that are relatively inexpensive. I have a Wessex Bombino Eb tuba (4 valve compensating) that I bought new for quite a bit less than $3K a couple or so years ago. I think they are now just under $3K for the lacquered version.
If you are a seasoned trombone player, then you probably can play tenor clef fluently. If so, you should be able to read tuba music and play it on the Eb without too much trouble. And if you read treble clef, even easier, because you can read tuba music (which is written in concert pitch and bass clef) by reading it as if it were treble clef with 3 additional sharps. If you read tenor clef, almost as easy.
Wessex builds some nice horns and for the money, you really get a lot. Plus they stand behind them and do a rather extensive quality control on each horn before it leaves the factory (in China).
If it is the school that wants you to cover the tuba part, have them loan you one so you can try it out before buying. Phooey on them if they won't. COVID or not, you can clean a mouthpiece (and a horn if you had to) so that you can play it. Unless you have to share the tuba, then I can understand their reluctance to loan it.
Good luck, and happy hunting.
John Morgan
The U.S. Army Band (Pershing's Own) 1971-1976
Adams E3 Custom Series Euphonium, Wessex EP-100 Dolce Euphonium, 1956 B&H Imperial Euphonium
Adams TB1 Tenor Trombone, Yamaha YBL-822G Bass Trombone
Kingdom of the Sun (KOS) Concert Band, Ocala, FL (Euphonium)
KOS Brass Quintet (Trombone, Euphonium)
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